Context. Chance-aligned sources or blended companions can cause false positives in planetary transit detections or simply bias the determination of the candidate properties. In the era of high-precision space-based photometers, the need for high spatial resolution images has been demonstrated to be critical for validating and confirming transit signals. This already applied to the Kepler mission, is now applicable to the TESS survey, and will be critical for the PLATO mission. Aims. In this paper we present the results of the AstraLux-TESS survey, a catalog of high spatial resolution images obtained with the AstraLux instrument at the Calar Alto observatory (Almería, Spain) in the context of the TESS Follow-up Observing Program. Methods. We used the lucky imaging technique to obtain high spatial resolution images from planet candidate hosts included mostly in two relevant regimes: exoplanet candidates belonging to the level one requirement of the TESS mission (planets with radii R < 4 R_⊕) and TESS planet candidates around intermediate-mass main-sequence stars. Results. Among the 185 planet host candidate stars observed, we found 13 (7%) to be accompanied by additional sources within a separation of 2.2 arcsec. Among them, six are not associated with sources in the Gaia DR3 catalog, thus contaminating the TESS light curve. Even if no contaminants have been detected, we can provide upper limits and probabilities to the possible existence of field contaminants through the sensitivity limits of our images. Among the isolated hosts, we can discard hazardous companions (bright enough to mimic a planetary transit signals) with an accuracy below 1% for all their planets. Conclusions. The results from this catalog are key to the statistical validation of small planets (prime targets of the TESS mission) and planets around intermediate-mass stars in the main sequence. These two populations of planets are difficult to confirm with the radial velocity technique because of the shallow amplitude of small planets and the high rotational velocities and low number of available spectral lines in the intermediate stellar mass regime. Our results also demonstrate the importance of this type of follow-up observation for future transit missions such as PLATO, even in the Gaia era.